VIBRATIONAL PROPERTIES OF A CONTINUOUS SELF-SIMILAR STRUCTURE

We present an extensive investigation of the normal modes of vibration of a prototype hierarchical continuous system, consisting of a Cantor -like sequence of piezoelectric and resin elements. From a detailed an alysis of the density of states, displacement profiles, and eigenvalue -spacing distributions, evidence is found for the existence of multipl e fracton and phonon regimes. The role of resonant modes and the effec t of disorder, which may be of primary importance in real systems, are also discussed in detail.